I think he is referring to Newton's form of the binominal theorem for the absolute value of n less than 1.
Something like[tex] \sqrt{x+1}= x+\frac{1}{2x}-\frac{1}{8x^3}+-[/tex] In the case of x=5^2, we can expand like
[tex]\sqrt{5^2+1} = 5+1/10-1/1000+-+ =5 +99/1000 =5.099 +-+[/tex] This is sometimes a convient way to get rough answers mentally.